Mesh deform a curve with shape keys
A curve is defined by a number of points and the connection between each point is then calculated. Any deform modifier on a curve can only move the points that define the curve, it cannot distort the curve in-between two curve points.

To get the benefits of a mesh deform modifier on a curve you need to be sure that the areas of the mesh that are deformed by shapekeys are surrounding a point in the curve.